Measuring the effect of different political actions to contrast the contagion of COVID19
Angela Andreella, Michele Lambardi, Silvia De Nicolò
03th June, 2020
1 Introduction
Since the beginning of the COVID-19 epidemic, policymakers in different countries have introduced different political action to contrast the contagion. The containment restrictions span from worldwide curfews, stay-at-home orders, shelter-in-place orders, shutdowns/lockdowns to softer measures, and stay-at-home recommendations and including, besides the development of contact tracing strategies and specific testing policies. The pandemic has resulted in the largest amount of shutdowns/lockdowns worldwide at the same time in history.
The timing of the different interventions concerning the spread of the contagion both at a global and intra-national level has been very different from country to country. The between-countries variability, in combination with demographical, economic, health-care-related, and area-specific factors, has resulted in different contagion patterns across the world.
Therefore, our goal is two-fold. The aim is to measure the effect of the different political actions by analyzing and comparing types of actions from a global perspective and, at the same time, to benchmark the effect of the same action in a heterogeneous framework such as the Italian regional context.
different regions of Italy.
2 Data
The data used in this analysis refer to mainly two open datasets, i.e., the COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University for contagion data (Dong, Du, and Gardner (2020)) and Oxford COVID-19 Government Response Tracker (OxCGRT) for policies tracking (Thomas et al. (2020)).
3 Containment strategies and resembling patterns
4 Effect of policies from a global perspective
Some countries have underestimated the dangerousness of the Coronavirus disease 2019 (COVID-19) and the importance of applying the containment measures. The little concern of some countries regarding the COVID-19 infectious disease is due to many and different reasons. Some countries decided to save the economy instead of people’s lives, i.e., it is a method to fight a war; in this case, the pandemic war.
For that, we want to analyze which countries adopt the ``optimal’’ policy measures to contain the contagion of COVID-19. Thanks to the Thomas et al. (2020) data sets, we know which type of measures each government takes and when. The indicators of government response considered are \(17\) in total, that can be resumed in indicators of a lockdown/social distancing, contact tracing, movement restrictions, testing policy, public health measures, and governance and socio-economic measures.
Therefore, some variables as the number of hospital beds are considered from OECD to have some additional covariates that can influence the variation in government responses to COVID-19.
We restrict the full range of responses to COVID-19 from governments around the countries analyzed in Section 3, i.e., Korea, Singapore, Germany, Canada, Sweden, Greece, Portugal, Spain, United States of America, Irland, United Kingdom, Italy, Netherlands, Austria, Switzerland, Finland, Norway, Denmark, and France.
The daily number of active persons is analyzed as a measure of the COVID-19 situation. Being a count variable, we decide to use a Negative Binomial Regression to correct also for the possible overdispersion. Therefore, the hierarchical structure is induced by the nested structure of countries inside the clusters and by the statement of the repeated measure. For that, we decide to use a generalized mixed model with family negative binomial. The country’s information and the clusters and date information, are used as random effects in our model.
So, the aim is to understand how the lockdown policies influence the contagions. We consider the aligned data concerning the first confirmed case, and we have the following situation:
Also, we lag the number of active respect to \(14\) days, considering the influences of the restrictions imposed at time \(t\) on the number of active at time \(t+14\), to make a correct impact. The observations are aligned concerning the first confirmed case across the countries to have observations directly comparable from a longitudinal point of view.
4.1 Exploratory Analysis
The set of covariates considered in this analysis can be divided into three main areas:
Longitudinal economic variables;
Longitudinal health system variables;
Fixed demographic/economic/health variables.
4.1.1 Economic Variables
| Name | Measurement | Description |
|---|---|---|
| Income Support | Ordinal | Government income support to people that lose their jobs |
| Debt/contract relief for households | Ordinal | Government policies imposed to freeze financial obligations |
| Fiscal measures | USD | Economic fiscal stimuli |
| International support | USD | monetary value spending to other countries |
We combine these two first economic variables into one continuous variable using the Polychoric Principal Component Analysis, to diminish the number of covariates inside the model, having \(9\) ordinal policies lockdown covariates.
Therefore, the USD’s two economic variables are examined and transformed into a logarithmic scale to de-emphasize very large values.
For further details about the definition of the economic variables, please see the BSG Working Paper Series
4.1.2 Demographic/Fixed variables
We analyze various variables from the World Bank Open Data that are fixed along the temporal dimension:
| Name | Measurement |
|---|---|
| Population | Numeric |
| Population ages 65 and above (% of total population) | Numeric |
| Population density (people per sq. km of land area) | Numeric |
| Hospital beds (per 1,000 people) | Numeric |
| Death rate, crude (per 1,000 people) | Numeric |
| GDP growth (annual %) | Numeric |
| Urban population (% of total population) | Numeric |
| Surface area (sq. km) | Numeric |
4.1.3 Health variables
We analyze two heatlh systems variables.
| Name | Measurement | Description |
|---|---|---|
| Emergency Investment in healthcare | USD | Short-term spending on, e.g, hospitals, masks, etc |
| Investment in vaccines | USD | Announced public spending on vaccine development |
Also, in this case, we transform the set of healthy variables into one continuous variable using the Polycorin Principal Component Analysis.
4.2 Model
The data are observed for each country nested within the temporal date. We are also considering the Clusters variable. Therefore we have a three-level structure of the data. Therefore, the variability of the data comes from nested sources: countries are nested within clusters where the measures of the observations are repeated across time, i.e., longitudinal data.
For that, the mixed model approach is considered to exploit the different types of variability coming from the hierarchical structure of our data. Firstly, the Intraclass correlation coefficient (ICC) is computed:
\[ ICC_{date; active} = 0.0936 \quad ICC_{Countries; Active} = 0.4015 \quad ICC_{Clusters; Active} = 0.0951 \]
Therefore, the \(40.15\%\) of the data’s variance is given by the random effect of the countries, while the \(9.36\%\) by the temporal effect and \(9.51\%\) by the clusters effect. Therefore, the mixed model impose of sure a random effect for the countries; the other two effects is selected using the conditional AIC.
The random effects are used to model multiple sources of variations and subject-specific effects, and thus avoid biased inference on the fixed effects. The dependent variable is the cumulated number of active persons; therefore, a count data model is considered. To control the overdispersion of our data, i.e., the conditional variance exceeds the conditional mean, the negative binomial regression with Gaussian-distributed random effects is performed using the glmmTMB R package developed by Brooks et al. (n.d.). Let \(n\) countries, and country \(i\) is measured at \(n_i\) time points \(t_{ij}\). The active person \(y_{ij}\) count at time \(t+14\), where \(i=1,\dots, n\) and \(j = 1, \dots,n_i\), follows the negative binomial distribution:
\[y_{ij} \sim NB(y_{ij}|\mu_{ij}, \theta) = \dfrac{\Gamma(y_{ij}+ \theta)}{\Gamma(\theta) y_{ij}!} \cdot \Big(\dfrac{\theta}{\mu_{ij} + \theta}\Big)^{\theta}\cdot \Big(\dfrac{\mu_{ij}}{\mu_{ij} + \theta}\Big)^{y_{ij}}\] where \(\theta\) is the dispersion parameter that controls the amount of overdispersion, and \(\mu_{ij}\) are the means. The means \(\mu_{ij}\) are related to the host variables via the logarithm link function:
\[\log(\mu_{ij}) = \log(T_{ij}) + X_{ij} \beta + Z_{ij} b_i \quad b_i \sim \mathcal{N}(0,\psi)\]
where \(\log(T_{ij})\) is the offset that corrects for the variation of the count of the active person at time \(t\). \(\text{E}(y_{ij}) = \mu\) and \(\text{Var}(y_{ij}) = \mu (1 + \mu\phi)\) from Hardin and Hilbe (2018).
After some covariates selection steps and random effects selection, the final model is expressed as:
summary(mod1)## Family: nbinom2 ( log )
## Formula:
## active_lag ~ pca_EC + pop_density_log + surface_area_log + pca_hs +
## workplace_closingF + gatherings_restrictionsF + transport_closingF +
## stay_home_restrictionsF + testing_policyF + contact_tracingF +
## Clusters + (0 + pca_LD | id) + (1 | date2) + (1 | Clusters)
## Data: dat
## Offset: log(active + 1)
##
## AIC BIC logLik deviance df.resid
## 40748.6 40921.6 -20344.3 40688.6 2330
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## id pca_LD 2.928e-01 5.411e-01
## date2 (Intercept) 4.169e+00 2.042e+00
## Clusters (Intercept) 4.215e-09 6.492e-05
## Number of obs: 2360, groups: id, 20; date2, 158; Clusters, 5
##
## Overdispersion parameter for nbinom2 family (): 1.07
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.95466 0.70894 -1.347 0.17811
## pca_EC -0.53735 0.07044 -7.629 2.37e-14 ***
## pop_density_log 0.15443 0.04620 3.342 0.00083 ***
## surface_area_log 0.05360 0.03587 1.494 0.13510
## pca_hs 0.05193 0.02029 2.559 0.01050 *
## workplace_closingF1 -0.24604 0.14061 -1.750 0.08016 .
## workplace_closingF2 -1.12441 0.14061 -7.997 1.28e-15 ***
## workplace_closingF3 -0.46986 0.17228 -2.727 0.00638 **
## gatherings_restrictionsF1 -0.52789 0.16317 -3.235 0.00122 **
## gatherings_restrictionsF2 -1.22558 0.14231 -8.612 < 2e-16 ***
## gatherings_restrictionsF3 -1.48631 0.17392 -8.546 < 2e-16 ***
## gatherings_restrictionsF4 -1.67393 0.17987 -9.306 < 2e-16 ***
## transport_closingF1 -0.04257 0.10635 -0.400 0.68897
## transport_closingF2 -0.44643 0.20266 -2.203 0.02761 *
## stay_home_restrictionsF1 -0.06059 0.10879 -0.557 0.57758
## stay_home_restrictionsF2 -0.13755 0.14964 -0.919 0.35799
## stay_home_restrictionsF3 -0.87098 0.29387 -2.964 0.00304 **
## testing_policyF1 0.20317 0.09147 2.221 0.02633 *
## testing_policyF2 0.55401 0.11289 4.908 9.21e-07 ***
## testing_policyF3 1.30708 0.16002 8.168 3.13e-16 ***
## contact_tracingF1 0.20257 0.08292 2.443 0.01456 *
## contact_tracingF2 0.37629 0.09576 3.929 8.51e-05 ***
## ClustersCl2 1.47291 0.17353 8.488 < 2e-16 ***
## ClustersCl3 1.93534 0.15847 12.213 < 2e-16 ***
## ClustersCl4 2.34541 0.14849 15.795 < 2e-16 ***
## ClustersCl5 2.43211 0.16041 15.162 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
5 Italian lockdown and regional outcomes
6 Supplementary materials
All the codes used for this analysis is available on Github.
Brooks, M. E., K. Kristensen, K. J. van Benthem, A. Magnusson, C. W. Berg, A. Nielsen, H. J. Skaug, M. Mächler, and B. Bolker. n.d. “GlmmTMB Balances Speed and Flexibility Among Packages for Zero-Inflated Generalized Linear Mixed Modeling.” The R Journal 9 (2): 378–400.
Dong, E., H. Du, and L. Gardner. 2020. “An Interactive Web-Based Dashboard to Track Covid-19 in Real Time.” Lancet Infect Dis.
Hardin, J. W., and J. M. Hilbe. 2018. Generalized Linear Models and Extensions. 4th ed. Stata Press.
Thomas, H., S. Webster, A. Petherick, T. Phillips, and B. Kira. 2020. “Oxford Covid-19 Government Response Tracker, Blavatnik School of Government.” Data Use Policy: Creative Commons Attribution CC BY Standard.